Scale Effect on Dynamic Analysis of Electrostatically Actuated Nano Beams Using the Nonlocal-Gradient Elasticity Theory

2013 ◽  
Vol 411-414 ◽  
pp. 1859-1862
Author(s):  
Liu Yang ◽  
Jian She Peng
Keyword(s):  
Dynamic Analysis ◽  
Elasticity Theory ◽  
Scale Effect ◽  
Gradient Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Beam Model ◽  
Electrostatically Actuated

A nonlocal-gradient elasticity beam model with two independent gradient coefficients based on the classical nonlocal elasticity theory and strain gradient theory is used to study dynamic analysis of electrostatically actuated nanobeams. The numerical results show that the deflection response and frequency response of nanobeams are all affected by the small scale. And the two independent gradient coefficients play the different roles in it. This paper broadens the way of studying scale effect.

Pull-In Instability of Electrostatically Actuated Nano-Beams Using the Nonlocal-Gradient Elasticity Theory

2014 ◽  
Vol 488-489 ◽  
pp. 1256-1259
Author(s):  
Jian She Peng ◽  
Liu Yang
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Gradient Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Beam Model ◽  
Electrostatically Actuated ◽  
Gradient Elasticity Theory

A nonlocal-gradient elasticity beam model with two independent gradient coefficients based on the classical nonlocal elasticity theory and strain gradient theory is used to study the pull-in instability of electrostatically actuated nanobeams. The numerical results show that the pull-in voltage of nanobeams are affected by the small scale. And the two independent gradient coefficients play the different roles in it. This paper broadens the way of studying scale effect.

Local gradient Bernoulli–Euler beam model for dielectrics: effect of local mass displacement on coupled fields

2020 ◽  
pp. 108128652096337
Author(s):  
Olha Hrytsyna
Keyword(s):  
Strain Gradient Theory ◽  
Beam Deflection ◽  
Small Scale ◽  
Gradient Theory ◽  
Beam Model ◽  
Euler Beam ◽  
Local Mass ◽  
Mass Displacement ◽  
Local Mass Displacement ◽  
Local Gradient

The size-dependent behaviour of a Bernoulli–Euler nanobeam based on the local gradient theory of dielectrics is investigated. By using the variational principle, the linear stationary governing equations of the local gradient beam model and corresponding boundary conditions are derived. In this set of equations the coupling between the strain, the electric field and the local mass displacement is taken into account. Within the presented theory, the process of local mass displacement is associated with the non-diffusive and non-convective mass flux related to the changes in the material microstructure. The solution to the static problem of an elastic cantilever piezoelectric beam subjected to end-point loading is used to investigate the effect of the local mass displacement on the coupled electromechanical fields. The obtained solution is compared to the corresponding ones provided by the classical theory and strain gradient theory. It is shown that the beam deflection predicted by the local gradient theory is smaller than that by the classical Bernoulli–Euler beam theory when the beam thickness is comparable to the material length-scale parameter. The obtained results also indicate that the piezoelectricity has a significant influence on the electromechanical response in a dielectric nanobeam. The presented mathematical model of the dielectric beam may be useful for the study of electromechanical coupling in small-scale piezoelectric structures.

NONLOCAL THEORY FOR BUCKLING OF NANOPLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 411-429 ◽  
Author(s):  
S. C. PRADHAN ◽  
J. K. PHADIKAR
Keyword(s):  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Theoretical Development ◽  
Small Scale ◽  
Classical Plate Theory ◽  
Small Scale Effect

Classical plate theory (CLPT) and first-order shear deformation plate theory (FSDT) of plates are reformulated using the nonlocal elasticity theory. Developed nonlocal plate theories have been applied to study buckling behavior of nanoplates. Nonlocal elasticity theory, unlike traditional elasticity theory introduces a length scale parameter into the formulation to take into account the discrete structure of the material to some extent. Both single-layered and multilayered nanoplates have been included in the analysis. Navier's approach has been used to obtain exact solutions for buckling loads for simply supported boundary conditions. Dependence of the small scale effect on various geometrical and material parameters has been investigated. Present study reveals the presence of significant small scale effect on the buckling response of nanoplates. The theoretical development and the numerical results presented in the present work are expected to promote the use of nonlocal theories for more accurate prediction of stability behavior of nanoplates and nanoshells.

CALIBRATION OF NONLOCAL SCALE EFFECT PARAMETER FOR BENDING SINGLE-LAYERED GRAPHENE SHEET UNDER MOLECULAR DYNAMICS

NANO ◽  
2012 ◽  
Vol 07 (05) ◽  
pp. 1250033 ◽  
Author(s):  
L. Y. HUANG ◽  
Q. HAN ◽  
Y. J. LIANG
Keyword(s):  
Molecular Dynamics ◽  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Md Simulations ◽  
Small Scale ◽  
Graphene Sheets ◽  
Small Scale Effect ◽  
Effect Parameter

In this article, the small scale effect parameter e0 of single-layered graphene sheets (SLGSs) is calibrated for the bending problem. Taking the SLGSs as a rectangular plate, the normal displacement of the simply supported plate under concentrated force was analyzed by both nonlocal elasticity theory and molecular dynamics (MD) simulations, then the small scale effect parameter e0 of SLGSs with different size was obtained by matching the displacement of the nonlocal elasticity theory and that obtained from MD simulations. The results show that the value of e0 is not a constant but has a relationship with the size of SLGSs, and the relationship of armchair-graphene sheets and zigzag-graphene sheets is different.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

Mechanical Behavior of Functionally Graded Nano-Cylinders Under Radial Pressure Based on Strain Gradient Theory

2018 ◽  
Vol 35 (4) ◽  
pp. 441-454 ◽  
Author(s):  
M. Shishesaz ◽  
M. Hosseini
Keyword(s):  
Mechanical Behavior ◽  
Strain Gradient ◽  
Material Properties ◽  
Scale Effects ◽  
Radial Pressure ◽  
Functionally Graded ◽  
High Order ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory

ABSTRACTIn this paper, the mechanical behavior of a functionally graded nano-cylinder under a radial pressure is investigated. Strain gradient theory is used to include the small scale effects in this analysis. The variations in material properties along the thickness direction are included based on three different models. Due to slight variations in engineering materials, the Poisson’s ratio is assumed to be constant. The governing equation and its corresponding boundary conditions are obtained using Hamilton’s principle. Due to the complexity of the governed system of differential equations, numerical methods are employed to achieve a solution. The analysis is general and can be reduced to classical elasticity if the material length scale parameters are taken to be zero. The effect of material indexn, variations in material properties and the applied internal and external pressures on the total and high-order stresses, are well examined. For the cases in which the applied external pressure at the inside (or outside) radius is zero, due to small effects in nano-cylinder, some components of the high-order radial stresses do not vanish at the boundaries. Based on the results, the material inhomogeneity indexn, as well as the selected model through which the mechanical properties may vary along the thickness, have significant effects on the radial and circumferential stresses.

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